# Efficient Globally Convergent Stochastic Optimization for Canonical Correlation Analysis

arXiv: https://arxiv.org/abs/1604.01870 · HTML: https://mlsanity.com/paper/1604.01870/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Apr 2016.

## Built on by (most cited first, 4 of 4)

- [An Online Riemannian PCA for Stochastic Canonical Correlation Analysis](https://mlsanity.com/paper/2106.07479/) (2021)
- [Optimization without Retraction on the Random Generalized Stiefel Manifold](https://mlsanity.com/paper/2405.01702/) (2024)
- [Faster Randomized Methods for Orthogonality Constrained Problems](https://mlsanity.com/paper/2106.12060/) (2021)
- [The Symmetric Generalized Eigenvalue Problem as a Nash Equilibrium](https://mlsanity.com/paper/2206.04993/) (2022)

## Abstract (arXiv)

We study the stochastic optimization of canonical correlation analysis (CCA), whose objective is nonconvex and does not decouple over training samples. Although several stochastic gradient based optimization algorithms have been recently proposed to solve this problem, no global convergence guarantee was provided by any of them. Inspired by the alternating least squares/power iterations formulation of CCA, and the shift-and-invert preconditioning method for PCA, we propose two globally convergent meta-algorithms for CCA, both of which transform the original problem into sequences of least squares problems that need only be solved approximately. We instantiate the meta-algorithms with state-of-the-art SGD methods and obtain time complexities that significantly improve upon that of previous work. Experimental results demonstrate their superior performance.